Question # a) There are classes of 234 students, find the mean and standart deviation for the number born on the 4th of July.The value of the mean is mu =?

Probability
ANSWERED a) There are classes of 234 students, find the mean and standart deviation for the number born on the 4th of July. Ignore leap years.The value of the mean is $$\displaystyle\mu$$ = (Round to six decimal places as needed)
Yhe value of the standart deviation is $$\displaystyle\sigma$$ = (Round to six decimal places as needed)
b) In a class of 234 students, would two be an unusually high number who were born on the 4th of July? Would 2 be an unussually high number of individuals who were born on the 4th of July?
A. This result is unlikely because 2 is within the range of usual values.
B. No, because 2 is within the range of usual values.
C. Yes, because 2 is greater than the maximum usual value.
D. Yes, because 2 is below the minimum usual value. 2021-08-09

a) Probability of being born on 4th of July is $$\displaystyle{\frac{{{1}}}{{{365}}}}$$
Here n = 234
Mean $$\displaystyle{n}{p}={234}\cdot{\frac{{{1}}}{{{365}}}}={0.642}$$
Standart deviation $$\displaystyle=\sqrt{{{n}{p}{a}}}=\sqrt{{{234}\cdot{\frac{{{1}}}{{{365}}}}\cdot{\frac{{{364}}}{{{365}}}}}}=\sqrt{{{234}\cdot{0.003}\cdot{0.998}}}=\sqrt{{{0.7006}}}={0.838}$$
b) P (2students born on the 4th of July) $$\displaystyle={234}\cdot{\left({\frac{{{1}}}{{{365}}}}\right)}^{{2}}={7.907}\cdot{234}={0.0017}{<}{0.05}$$
It would be unusual to have two individuals born on the 4th of july
С is correct because 2 is greater than the maximum usual value